Comparison methods for fitting data using Johnson translation distributions
WSC '88 Proceedings of the 20th conference on Winter simulation
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Moment matching and percentile matching are the standard methods for fitting a distribution from Johnson's translation system (the SL, S U, S B, and S N families) to a univariate data set (Johnson and Kotz 1970). One method for fitting a multivariate Johnson distribution to a vector-valued data set is to: (a) fit each marginal distribution separately with a univariate Johnson distribution; and then (b) fit a multivariate normal distribution to the transformed vectors using the sample correlation coefficients between the transformed coordinates. To make this approach numerically feasible, Wilson (1983) implemented an interactive percentile matching algorithm based on a modified Newton-Raphson procedure. When the algorithm was applied to 80 trivariate data sets arising in a large-scale policy analysis project, excessive manual intervention was required in some situations to obtain acceptable fits (Martin 1983).